100a-a^2-1234=0

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Solution for 100a-a^2-1234=0 equation:


Simplifying
100a + -1a2 + -1234 = 0

Reorder the terms:
-1234 + 100a + -1a2 = 0

Solving
-1234 + 100a + -1a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1234 + -100a + a2 = 0

Move the constant term to the right:

Add '-1234' to each side of the equation.
1234 + -100a + -1234 + a2 = 0 + -1234

Reorder the terms:
1234 + -1234 + -100a + a2 = 0 + -1234

Combine like terms: 1234 + -1234 = 0
0 + -100a + a2 = 0 + -1234
-100a + a2 = 0 + -1234

Combine like terms: 0 + -1234 = -1234
-100a + a2 = -1234

The a term is -100a.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100a + 2500 + a2 = -1234 + 2500

Reorder the terms:
2500 + -100a + a2 = -1234 + 2500

Combine like terms: -1234 + 2500 = 1266
2500 + -100a + a2 = 1266

Factor a perfect square on the left side:
(a + -50)(a + -50) = 1266

Calculate the square root of the right side: 35.580893749

Break this problem into two subproblems by setting 
(a + -50) equal to 35.580893749 and -35.580893749.

Subproblem 1

a + -50 = 35.580893749 Simplifying a + -50 = 35.580893749 Reorder the terms: -50 + a = 35.580893749 Solving -50 + a = 35.580893749 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + a = 35.580893749 + 50 Combine like terms: -50 + 50 = 0 0 + a = 35.580893749 + 50 a = 35.580893749 + 50 Combine like terms: 35.580893749 + 50 = 85.580893749 a = 85.580893749 Simplifying a = 85.580893749

Subproblem 2

a + -50 = -35.580893749 Simplifying a + -50 = -35.580893749 Reorder the terms: -50 + a = -35.580893749 Solving -50 + a = -35.580893749 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + a = -35.580893749 + 50 Combine like terms: -50 + 50 = 0 0 + a = -35.580893749 + 50 a = -35.580893749 + 50 Combine like terms: -35.580893749 + 50 = 14.419106251 a = 14.419106251 Simplifying a = 14.419106251

Solution

The solution to the problem is based on the solutions from the subproblems. a = {85.580893749, 14.419106251}

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